Ratio of 9th grade students to 10th grade students

Question

I've been pondering on this question and I realize my understanding of percentages are probably weak so please help guide me through. Let's say 9th grade is 70% girls and tenth grade is 30% girls. If 40% of all ninth and tenth grade students are girls, what is the ratio of the number of 9th grade students to 10th grade students. So this is from my understanding: I think 70 out of 100 students are girls in gr 9, and 30 out of 100 girls in gr 10. Then this means total number of students in gr 9 and 10 would be 200 so 40% of that is 80 students. But I don't know where to go from here and I feel like it doesn't add up...Please explain what is wrong with my thinking and how I should be thinking! Thank you!!

Answer 1

The problem with your answer is that you're implicitly assuming the ratio of students in the two classes to be $1:1$. (Are you able to see that?)

Here's how to go about it:

Let the number of students in $9^{th}$ grade be $x$ and $10^{th}$ grade be $y$.

$$G_9 = 0.7x$$

$$G_{10} = 0.3y$$

$$G = G_9 + G_{10} = 0.4(x+y)$$

Notation:

$G_9$: girls in $9^{th}$ grade.

$G_{10}$: girls in $10^{th}$ grade.

$G$: Total girls

Solve for $\frac{x}{y}$!